Question

Assume the grades has Normal distribution with the mean of 70, and the standard deviation of 15. Answer the following questions 1. Calculate 10t 25t* 50 75t and 90* percentiles once by converting to the standard Normal distribution, and again directly (using the non-standard Normal distribution) 2. What percentage of students score between 80 and 90 in the exam? 3. What percentage of students fail? 4. What percentage of students pass with A? 5. Generate a sample of size 16 from this distribution and construct 90%, 95%, 98%, and 99% confidence intervals (CI) for true mean. Notice that all grades in the sample must be valid grades between 0 and 100. Which CI's contain the true mean? 6. Generate 20 samples of size 16 from this distribution. Calculate the absolute error of estimate. Plot both the error of the estimate and the absolute error of estimate. 7. Take samples of size 16, 25, 36, 49, 64, 81, and 100 and plot the standard error of sample mean. Do you observe a trend? Explain your observation 8. Truncate this Normal distribution between 40 and 100 and normalize it to have a valid density function. Use four (4) decimal points and notice that the total probability of the truncated distribution must be equal to one.

Answer 1

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